We study the buildup of the spatial correlation in a two-dimensional dissipative Rydberg system using the time-dependent variational principle. We find that in the sweeping process of the Rabi frequency and detuning, a moderately large decay rate induced by the two-photon excitation scheme suppresses significantly the buildup of correlation in a long-time scale in agreement with experimental results. A relatively large dephasing rate leads to a short relaxation time for the antiferromagnetic correlation to reach a stable value. These results provide a general view about the role of various decoherence mechanisms in the buildup of antiferromagnetic correlations and guide experiments to explore dissipative many-body dynamics using a Rydberg atomic system.
We study the buildup of the spatial correlation in a two-dimensional dissipative Rydberg system using the time-dependent variational principle. We find that in the sweeping process of the Rabi frequency and detuning, a moderately large decay rate induced by the two-photon excitation scheme suppresses significantly the buildup of correlation in a long-time scale in agreement with experimental results. A relatively large dephasing rate leads to a short relaxation time for the antiferromagnetic correlation to reach a stable value. These results provide a general view about the role of various decoherence mechanisms in the buildup of antiferromagnetic correlations and guide experiments to explore dissipative many-body dynamics using a Rydberg atomic system.
Inevitably present in many current experiments with ultracold Rydberg atoms, dissipative effects such as dephasing and decay modify the dynamics of the examined system. In this thesis, the dynamics of many-body Rydberg systems in the incoherent regime is studied numerically. Specifically, a wave function Monte Carlo (MCWF) technique is integrated into a coherent two-level many-body Rydberg model, allowing a numerical simulation of dissipative dynamics. This model is used to benchmark a steady-state rate equation model and assess its range of validity. In addition, incoherent, off-resonant excitation dynamics is studied in a one-dimensional disordered geometry. We find that our simulation results can essentially be explained by the equilibration time scale as well as — for positive laser detuning — resonant excitations arising when the laser detuning compensates the Rydberg interaction. Eventually, we employ a rate equation model to investigate excitation spectra for an experimental trap geometry, which we benchmark using the MCWF technique. Based on numerical data, we deduce that in the considered parameter regime the dominant excitation mechanism can be characterized as sequential growth of aggregates of Rydberg excitations around an initial seed. Our simulation results highlight the impact of incoherent effects on observables such as Rydberg population, excitation number fluctuation and pair correlation function.
The effect of electromagnetically induced transparency (EIT) combined with Rydberg-state atoms provides high optical nonlinearity to efficiently mediate the photon-photon interaction. However, the decay rate of Rydberg coherence, i.e., the decoherence rate, plays an important role in optical nonlinear efficiency and can be largely influenced by laser frequency fluctuation. In this work, we carried out a systematic study of the effect of laser frequency fluctuation on the decoherence rate. We derive an analytical formula that quantitatively describes the relationship between the decoherence rate and laser frequency fluctuation. The formula is experimentally verified by using the $\mathrm{\ensuremath{\Lambda}}$-type EIT system of laser-cooled 87Rb atoms, in which one can either completely eliminate or controllably introduce the effect of laser frequency fluctuation. We also include the effect of Doppler shift caused by the atomic thermal motion in the formula, which can be negligible in the $\mathrm{\ensuremath{\Lambda}}$-type EIT experiment but significant in the Rydberg-EIT experiment. Utilizing the atoms of 350 $\ensuremath{\mu}\mathrm{K}$, we study the decoherence rate in the Rydberg-EIT system involving the state of $|32{D}_{5/2}\ensuremath{\rangle}$. The experimental data are consistent with the predictions from the formula. We are able to achieve a rather low decoherence rate of $2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}48$ kHz at a moderate coupling Rabi frequency of $2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}4.3$ MHz.
Based on the dipole blockade effect and with the aid of the superatom (SA) model, we propose a scheme to investigate the correlated evolution of two Rydberg sub-superatoms (SSAs), formed by two spatially separated atomic Rydberg sub-ensembles but in the same blockade region. Starting from the pure separable states, we investigate the in-phase or anti-phase correlated dynamics and explore how two Rydberg SSAs entangle with each other mediated by a single Rydberg excitation. Starting from the entangled states, we discuss the robustness of the system against decoherence induced by the dephasing rate. Our results show that both the correlated evolution of two Rydberg SSAs and their collective-state entanglement are usually sensitive to the number of each Rydberg SSA. This allows us to coherently manipulate the Rydberg ensemble over long distances from the single-quantum level to the mesoscopic level by changing the number of atoms. Furthermore, the method for dividing an SA into two SSAs and obtaining their spin operators without any approximation can be readily generalized to the case of many SSAs. It may have potential promising applications in quantum information processing and provide an attractive platform to study the quantum-classical correspondence, many-body physics and so on.
This thesis explores the effects of decoherence and dephasing on single- and many- body dynamics of spin-systems. A particular realisation of the spin systems that the work focuses on are highly excited, Rydberg states of atoms. A software library ARC (Alkali Rydberg Calculator) for calculating properties of Rydberg states in alkali metals is presented, with particular attention to the multi- atom and multi-level effects that influence many-body dynamics in realistic systems, and properties related to terahertz imaging with alkali atom Rydberg states. Dressed-state electromagnetically induced transparency (EIT) is proposed as a way of preparing uniform-phase spin-waves in ladder excitation schemes, making the collective excitation storage insensitive to motional dephasing. Proof of concept dressed state EIT experiments are presented. Strong resonant dressing is also theoretically analysed as a way of preparing velocity superposition of spin-waves. The developed theoretical model is in a good agreement with existing experimental data on single-photon many-atom quantum beats in diamond excitation schemes. By modelling the strongly driven Rydberg ensembles, many-body dynamics of driven-dissipative spin systems is analysed. Working in the limit of strong dephasing, the effects of fluctuations, the shape of interaction potential, spatial correlations and motion on non-equilibrium phase diagrams and the occurrence of bistability are examined. An ensemble averaged mean field model is introduced as an exact solution for completely uncorrelated ensembles. It is shown that the van der Waals interaction does not allow the occurrence of bistability, for which a finite dipolar core is required. The short-range interaction potential shape is found to have a profound influence on non-equilibrium phase diagrams, controlling the size of fluctuations in the dynamics. For a frozen system, several methods for identifying and quantifying bistable phases are introduced, and phase diagrams are reconstructed. It is shown that the temperature of external degrees of freedom, i.e. spin motion, can drive a non-equilibrium transition into the bistable phase.
The work presented in this dissertation concerns dynamics of Rydberg atom lattices in the presence of noise and dissipation. Rydberg atoms possess a number of exaggerated properties, such as a strong van der Waals interaction. The interplay of that interaction, coherent driving and decoherence leads to intriguing non-equilibrium phenomena. Here, we study the non-equilibrium physics of driven atom lattices in the presence of decoherence caused by either laser phase noise or strong decay. In the first case, we compare between global and local noise and explore their effect on the number of excitations and the full counting statistics. We find that both types of noise give rise to a characteristic distribution of the Rydberg excitation number. The main method employed is the Langevin equation but for the sake of efficiency in certain regimes, we use a Markovian master equation and Monte Carlo rate equations, respectively. In the second case, we consider dissipative systems with more general power-law interactions. We determine the phase diagram in the steady state and analyse its generation dynamics using Monte Carlo rate equations. In contrast to nearest-neighbour models, there is no transition to long-range-ordered phases for realistic interactions and resonant driving. Yet, for finite laser detunings, we show that Rydberg atom lattices can undergo a dissipative phase transition to a long-range-ordered antiferromagnetic phase. We identify the advantages of Monte Carlo rate equations over mean field predictions. Having studied the dynamics of Rydberg atom lattices, we study an application of the strong interactions in such systems for quantum information processing. We investigate the coherent exchange of a single photon between a superconducting microwave cavity and a lattice of strongly interacting Rydberg atoms in the presence of local electric field fluctuations plaguing the cavity surface. We show that despite the increased sensitivity of Rydberg states to electric fields, as compared to ground state atoms, the Rydberg dipole-dipole interaction can be used to protect the system against the dephasing induced by the local noise. Using 1/f and laser phase noise models, we show that compared to the case with non-interacting atoms, our system exhibits longer coherence lifetimes and larger retrieval efficiency of the photon after storing into the atoms.
We study the impact of dephasing on the excitation dynamics of a cloud of ultracold two-level Rydberg atoms for both resonant and off-resonant laser excitation, using the wave-function Monte Carlo technique. We find that while for resonant laser driving, dephasing mainly leads to an increase of the Rydberg population and a decrease of the Mandel Q parameter, at off-resonant driving strong dephasing toggles between direct excitation of pairs of atoms and subsequent excitation of single atoms, respectively. These two excitation mechanisms can be directly quantified via the pair-correlation function, which shows strong suppression of the two-photon resonance peak for strong dephasing. Consequently, qualitatively different dynamics arise in the excitation statistics for weak and strong dephasing in off-resonant excitation. Our findings show that time-resolved excitation number measurements can serve as a powerful tool to identify the dominating process in the system's excitation dynamics.